Two days to Petra and Dead Sea from Eilat tour itinerary:

you will be picked up anywhere from Eilat early morning, drive to the crossing border with Aqaba for 10 minutes, finish the formalities crossing the border to Jordan, then drive to Petra for two hours, where you will have guided tour in Petra for three hours exploring the old city center, stay the rest of the day in the old city climbing to one of the big monuments such as the monastery; by the sunset you return back to the visitors center then you will be delivered to your hotel in Petra, dinner and overnight in 3* stars hotel, you can change the accommodation into a Bedouin camp in little Petra this night

Day 2: Breakfast at the hotel or the camp - Drive to the Dead Sea - Lunch and relax at Dead Sea beach - Drive to Aqaba - drive to the border and cross back to Eilat:

you will have breakfast at the hotel in Petra, then drive to Dead Sea for two and half hours passing Dana nature reserve panoramic road overseeing the sandstone mountains underneath, around early afternoon you will arrive to Dead Sea private beach, enjoy swimming and relaxing at Dead Sea beach for 5 hours with open buffet lunch, then drive back to Aqaba if time allows to have short tour exploring Aqaba down town after that you will be transferred to the crossing border to return to Eilat, arriving the border around 7:00 pm

Physical rate: easy, hot in the summer (June, July, August) where you need good sun screen, and good hiking shoes for Petra tour